In the distillation column with a feed flow rate of $150$ kmol$/$h$,$ it is desired that $95\%$ of the B component be taken from the peak flow and $95\%$ of the C component from the base flow. Feed current mole fractions and relative volatility values $$of the four$-$component system are given in the table below. It is known that the column feed stream is saturated liquid. For this design:

a$)$ Identify light and heavy key components.

b$)$ Calculate the flow rates and component fractions of the peak and base flows.

c$)$ Calculate the minimum number of shelves, Nmin.

d$)$ Calculate the minimum rift rate, Rmin.

e$)$ Calculate the number of shelves, N$,$ where R $=1\mathrm{.}2$ x Rmin.

f$)$ Calculate the location of the feeding shelf, NF$\backslash$table$[[,\backslash$table$[[$Feed Flow$],[$Rate$]],\backslash$table$[[$feed$],[$relative$],[$volatility$]]],[$A$,0\mathrm{.}10,3\mathrm{.}9],[$B$,0\mathrm{.}35,2\mathrm{.}5],[$C$,0\mathrm{.}30,1\mathrm{.}6],[$D$,0\mathrm{.}25,1\mathrm{.}0]]$